Electrode to nerve distance estimation

ABSTRACT

Estimating a nerve-to-electrode distance involves applying a stimulus from a stimulus electrode to a nerve. Neural measurements of at least one evoked compound action potential are obtained, and processed in order to estimate an originating state of stimulation exhibiting at least one characteristic defined by a single fibre size. A single fibre model is then applied to produce a measure of the nerve-to-electrode distance. Also provided for is estimation of a distribution of recruited fibres. Measurements of a compound action potential are obtained from sense electrodes spaced apart along a neural pathway. A conduction velocity of the compound action potential is determined from the latency between the measurements. From the conduction velocity a dominant recruited fibre diameter is determined. A rate of dispersion of the compound action potential between the sense electrodes is determined. From the rate of dispersion a distribution of diameters of the recruited fibre population is determined.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a national stage of Application No.PCT/AU2016/050263, filed Apr. 8, 2016, which application claims thebenefit of Australian Provisional Patent Application No. 2015901270,filed Apr. 9, 2015, the disclosures of which are incorporated herein byreference in their entireties.

TECHNICAL FIELD

The present invention relates to neurostimulation, and in particularrelates to observing evoked compound action potentials caused byelectrical stimuli, in order to estimate a distance, or a change indistance, between a nerve and an electrode being used to stimulate thenerve.

BACKGROUND OF THE INVENTION

There are a range of situations in which it is desirable to apply neuralstimuli in order to give rise to a compound action potential (CAP). Forexample, neuromodulation is used to treat a variety of disordersincluding chronic pain, Parkinson's disease, and migraine. Aneuromodulation system applies an electrical pulse to tissue in order togenerate a therapeutic effect. When used to relieve chronic pain, theelectrical pulse is applied to the dorsal column (DC) of the spinalcord. Such a system typically comprises an implanted electrical pulsegenerator, and a power source such as a battery that may be rechargeableby transcutaneous inductive transfer. An electrode array is connected tothe pulse generator, and is positioned in the dorsal epidural spaceabove the dorsal column. An electrical pulse applied to the dorsalcolumn by an electrode causes the depolarisation of neurons, andgeneration of propagating action potentials. The fibres being stimulatedin this way inhibit the transmission of pain from that segment in thespinal cord to the brain. To sustain the pain relief effects, stimuliare applied substantially continuously, for example at 100 Hz.

Neuromodulation may also be used to stimulate efferent fibres, forexample to induce motor functions. In general, the electrical stimulusgenerated in a neuromodulation system triggers a neural action potentialwhich then has either an inhibitory or excitatory effect. Inhibitoryeffects can be used to modulate an undesired process such as thetransmission of pain, or to cause a desired effect such as thecontraction of a muscle.

For a number of reasons it is desirable to be able to determine thedistance of a nerve fibre responding to electrical stimulation from thestimulating electrode. Conventionally, spinal cord stimulation (SCS)delivers stimulation to the dorsal column at a fixed current. When asubject moves or changes posture the distance between the spinal cordand the implanted electrode array varies, resulting in an increase ordecrease in the amount of current received by the dorsal columns. Thesechanges in current result in changes to recruitment and paraesthesia,which can reduce the therapeutic effect of SCS and can create sideeffects including over-stimulation.

If a stimulus is of an amplitude and/or peak width and/or has otherparameter settings which put it below the recruitment threshold,delivery of such a stimulus will fail to recruit any neural response.Thus, for effective and comfortable operation, it is necessary tomaintain stimuli amplitude or delivered charge above the recruitmentthreshold. It is also necessary to apply stimuli which are below acomfort threshold, above which uncomfortable or painful percepts arisedue to increasing recruitment of Aδ fibres which are thinly myelinatedsensory nerve fibres associated with joint position, cold and pressuresensation. In almost all neuromodulation applications, a single class offibre response is desired, but the stimulus waveforms employed canrecruit action potentials on other classes of fibres which causeunwanted side effects, such as muscle contraction if motor fibres arerecruited. The task of maintaining appropriate stimulus amplitude ismade more difficult by electrode migration and/or postural changes ofthe implant recipient, either of which can significantly alter theneural recruitment arising from a given stimulus, depending on whetherthe stimulus is applied before or after the change in electrode positionor user posture. Postural changes alone can cause a comfortable andeffective stimulus regime to become either ineffectual or painful.

Another control problem, facing neuromodulation systems of all types, isachieving neural recruitment at a sufficient level required fortherapeutic effect, but at minimal expenditure of energy. The powerconsumption of the stimulation paradigm has a direct effect on batteryrequirements which in turn affects the device's physical size andlifetime. For rechargeable systems, increased power consumption resultsin more frequent charging and, given that batteries only permit alimited number of charging cycles, ultimately this reduces the implantedlifetime of the device.

Any discussion of documents, acts, materials, devices, articles or thelike which has been included in the present specification is solely forthe purpose of providing a context for the present invention. It is notto be taken as an admission that any or all of these matters form partof the prior art base or were common general knowledge in the fieldrelevant to the present invention as it existed before the priority dateof each claim of this application.

Throughout this specification the word “comprise”, or variations such as“comprises” or “comprising”, will be understood to imply the inclusionof a stated element, integer or step, or group of elements, integers orsteps, but not the exclusion of any other element, integer or step, orgroup of elements, integers or steps.

In this specification, a statement that an element may be “at least oneof” a list of options is to be understood that the element may be anyone of the listed options, or may be any combination of two or more ofthe listed options.

SUMMARY OF THE INVENTION

According to a first aspect the present invention provides a method ofestimating a nerve-to-electrode distance, the method comprising:

applying from a stimulus electrode to a nerve at least one stimulushaving defined stimulus parameters;

obtaining a plurality of neural measurements of at least one compoundaction potential evoked by the at least one stimulus;

processing the plurality of neural measurements in order to estimate anoriginating state of stimulation, the originating state of stimulationexhibiting at least one observable characteristic defined by a singlefibre size; and

applying a single fibre model to the estimated originating state ofstimulation and the stimulus parameters, in order to produce a measureof the nerve-to-electrode distance.

According to a second aspect the present invention provides animplantable device for estimating a nerve-to-electrode distance, thedevice comprising:

at least one stimulus electrode and at least one sense electrode;

measurement circuitry for obtaining a neural measurement from the oreach sense electrode; and

a processor configured to apply from the or each stimulus electrode to anerve at least one stimulus having defined stimulus parameters, obtainfrom the measurement circuitry a plurality of neural measurements of atleast one compound action potential evoked by the at least one stimulus,process the plurality of neural measurements in order to estimate anoriginating state of stimulation, the originating state of stimulationexhibiting at least one observable characteristic defined by a singlefibre size; and apply a single fibre model to the estimated originatingstate of stimulation and the stimulus parameters, in order to produce ameasure of the nerve-to-electrode distance.

The originating state of stimulation may be considered as a thresholdcondition of stimulation, at which a single fibre or a single fibre sizedominates or defines the nature of the evoked neural response. Thepresent invention recognises that by estimating the originating state ofstimulation, it is possible to isolate at least one characteristic whichis defined by a single fibre size. Knowledge of an evoked characteristicwhich is defined solely or largely by a single size of neural fibre inturn enables a single fibre model of recruitment to be applied, in orderto estimate the nerve-to-electrode distance. The present invention thusoperates to eliminate complicating effects arising from propagation of acompound action potential along a group of neural fibres of distinctsize.

Any suitable single fibre model may be applied to the originating stateof stimulation in order to produce the measure of nerve-to-electrodedistance. The single fibre model may comprise a lookup table matchingthe observed characteristic and the stimulus parameters to acorresponding nerve-to-electrode distance.

The measure of the nerve-to electrode distance may comprise an absolutemeasure of distance, or a relative measure reflecting a change indistance from a previous time, or a measure of a rate of change ofdistance.

In some embodiments of the invention, the method may comprise thefurther step of adjusting a therapeutic stimulus regime in response toan observed change in the nerve-to-electrode distance.

In some embodiments of the invention, the method may be performedintra-operatively, as part of a surgical procedure, for example toprogressively monitor a position of a structure bearing the electrodesrelative to the nerve. In some embodiments the method may be conductedas part of a postoperative fitting procedure of a neurostimulator.

In some embodiments of the invention the originating state ofstimulation may comprise an estimate of the ECAP peak width at thestimulus site. In such embodiments the applying comprises applying asingle stimulus in order to evoke a single ECAP, and the plurality ofneural measurements are obtained from at least two sense electrodes eachat a unique distance away from the stimulus electrode. Such embodimentsrecognise that an ECAP comprises a compound response made up ofcontemporaneous action potentials evoked on a plurality of individualnerve fibres, and that each nerve fibre exhibits a conduction velocitywhich depends at least partly on the diameter of that fibre, so that theECAP peak width widens at an approximately linear rate as eachindividual action potential propagates away from the stimulus site at aunique velocity. Such embodiments preferably estimate an originatingECAP peak width by extrapolating the first and second ECAP measures backto the stimulus site, given that a distance from the stimulus electrodeto the first and second sense electrodes is known. Such embodiments ofthe invention recognise that the originating ECAP peak width can beassumed to be dominated by that single fibre recruited at the stimulussite which had the broadest action potential peak width, typicallycomprising the recruited fibre of largest diameter as larger fibers aremore excitable than smaller diameter fibers. Such embodiments furtherrecognise that the nerve-to-electrode distance can in turn be estimatedfrom the originating ECAP peak width because of the dependence oforiginating ECAP dispersion upon the fibre to electrode distance.

Such embodiments, which estimate the originating ECAP peak width ordispersion, may be particularly suitable in applications where thestimulus and sense electrodes are well aligned alongside a neuralpathway, such as in the case of SCS.

The measure of ECAP peak width may comprise a half-height peak width,being a measure of a width of an ECAP peak as observed at an amplitudewhich is half the amplitude of the peak amplitude of the observed ECAPpeak. Alternatively the measure of ECAP peak width may comprise a timebetween the N1 and P1 peaks of the observed response, and/or a timebetween the P1 and P2 peaks. Alternatively the measure of ECAP peakwidth may comprise a time between a zero crossing preceding the N1 peakand a zero crossing following the N1 peak.

The ECAP peak width may be measured or assessed by extracting frequencycomponents of the neural measurements, for instance fast Fouriertransform. Preferably the neural measurements are first windowed toexclude discontinuities or like stimulus effects and/or measurementeffects. The frequency domain information of the respective neuralmeasurements may then be used to extract a measure of the dispersion.For example a profile of the frequency domain spectrum of the neuralmeasurements may be assessed for a roll-off or decay with frequency,whereby a faster roll-off of higher frequency components reflects a moredispersed ECAP peak, that is, a peak which is more dominated by lowerfrequency components. A slope or rate of decay of the frequency roll-offmay then be determined for each neural measurement, and used to estimatean originating state of stimulation namely the frequency roll-offpresent in the evoked response at the site of stimulation. Suchembodiments may be advantageous in measuring dispersion in noisy neuralmeasurements, as a frequency roll-off can be averaged or fitted over arelatively wide spectral range. Such embodiments may further beadvantageous in enabling a measure of dispersion to be obtained withoutreliance on the amplitude of the ECAP, for example in embodiments wheremanual user feedback or automated feedback operates to controlrecruitment at a substantially constant level.

The measure of ECAP peak width may comprise a function of one or moresuch measures, or may comprise any measure which reflects dispersion ofthe ECAP over time.

In some embodiments, neural measurements may be obtained of bothorthodromic and antidromic ECAPs, to permit an averaged or more robustestimate of the originating state of stimulation, and thus of thenerve-to-electrode distance estimate, to be obtained.

Additionally or alternatively, the originating state of stimulation mayin some embodiments comprise a stimulus threshold such as the Rheobase.In such embodiments, a stimulus threshold is preferably determined at atleast two differing stimulus pulse widths, from which the Rheobase canbe calculated. The conduction velocity is preferably measured and usedto determine a fibre diameter recruited at threshold. Fittedrelationships of the modelled single fibre Rheobase to theelectrode-to-nerve separation are then used to determine the separation.Such embodiments may be particularly advantageous in applicationsproviding or permitting only one measurement electrode, as may occur inthe brain which does not comprise a single longitudinal neural pathway.

The originating state of stimulation may in some embodiments beselectively explored in relation to a sub-population of fibres asdefined by refractory period. Such embodiments recognise that the fibreswithin the population of recruited fibres may have different refractoryperiods. The originating state of stimulation may be estimated inrelation to a specific sub-population of the fibres selected fordifferent refractory periods, for example by applying a stimulussequence comprising a first stimulus referred to as a masker stimuluswhich recruits all the fibres of interest, and then a short durationlater applying a second stimulus referred to as a probe stimulus. Theduration between the masker and probe stimuli is selected to be longerthan the refractory period of some fibres, but shorter than therefractory period of other fibres. Consequently, the probe stimulus willrecruit only those fibres having a short enough refractory period tohave recovered from the masker stimuli and able to be recruited a secondtime by the probe stimulus. In such embodiments the neural measurementsare then analysed specifically in relation to the portion of theobserved measurement which corresponds with the response evoked by theprobe stimulus.

Embodiments of the invention may thus be applied in neural stimulationapplications where the separation between the responding fibres and thestimulating electrode varies often or even continuously with patientmovement, whereby knowledge of the fibre-to-electrode distance or atleast of incremental changes thereof, would be valuable. Otherembodiments of the invention may be applied in relation to locatingresponding fibres three dimensionally in space in order to avoid orlocate them during a surgical or imaging procedure for example. Inanother application it is desirable to be able to locate a target fibreand position an electrode array in optimal position relative to thefibre in order to achieve the most effective stimulation. Suchembodiments may further comprise identifying a target nerve fasciclewithin a larger nerve bundle, at differing locations along the nervebundle, in order to detect variation in position of the fascicle withinthe bundle.

In some embodiments, the ECAP measurements are further used to estimatethe distribution of fiber diameters present in an ECAP. An indication ofthe distribution or spread of fiber diameters can provide a usefulvalidation for computer models and may be used to inform device andalgorithm design to improve outcomes for SCS.

Thus, according to a third aspect, the present invention provides amethod of estimating a distribution of fibres recruited by a stimulus,the method comprising

obtaining from at least two sense electrodes spaced apart along a neuralpathway respective measurements of a compound action potentialpropagating along the neural pathway;

determining a conduction velocity of the compound action potential fromthe latency between the measurements, and determining from theconduction velocity a dominant recruited fibre diameter;

determining a rate of dispersion of the compound action potentialbetween the sense electrodes, and determining from the rate ofdispersion a distribution of diameters of the recruited fibrepopulation.

According to a fourth aspect, the present invention provides a devicefor estimating a distribution of fibres recruited by a stimulus, thedevice comprising

at least one stimulus electrode and at least two sense electrodes,configured to be spaced apart along a neural pathway;

measurement circuitry for obtaining a neural measurement from each senseelectrode; and

a processor configured to obtain from the at least two sense electrodesrespective measurements of a compound action potential propagating alongthe neural pathway, determine a conduction velocity of the compoundaction potential from the latency between the measurements, determinefrom the conduction velocity a dominant recruited fibre diameter,determine a rate of dispersion of the compound action potential betweenthe sense electrodes, and determine from the rate of dispersion adistribution of diameters of the recruited fibre population.

In embodiments of the third and fourth aspects of the invention, therate of dispersion may be determined in any suitable manner describedherein, including any one or more of the observed ECAP peak width, ECAPpeak spacing, ECAP zero crossings, ECAP half-height peak width or ECAPspectral content.

The third and fourth aspects of the invention recognize that the overalldistribution of fibre diameters, the distribution of fibre diametersrecruited by a given stimulus, and/or the recruited fibres' conductionvelocities may vary from one subject to the next. Moreover, someembodiments further recognize that variations in such characteristicsmay be correlated with the neurological condition which brought aboutthe need for neurostimulation: for example, changes in conductionvelocity and distribution of fibre diameters in dorsal columns have beenrecorded in mouse models of neuropathic pain as a result of centralsensitization. Some embodiments of the third and fourth aspects of thepresent invention may thus further comprise treating the neurologicalcondition by administering or modifying a therapy in a manner responsiveto the determined distribution of diameters of the recruited fibrepopulation, or responsive to a change in the determined distributionover time.

According to a further aspect the present invention provides anon-transitory computer readable medium for estimating anerve-to-electrode distance, comprising instructions which, whenexecuted by one or more processors, causes performance of the following:

applying from a stimulus electrode to a nerve at least one stimulushaving defined stimulus parameters;

obtaining a plurality of neural measurements of at least one compoundaction potential evoked by the at least one stimulus;

processing the plurality of neural measurements in order to estimate anoriginating state of stimulation, the originating state of stimulationexhibiting at least one observable characteristic defined by a singlefibre size; and

applying a single fibre model to the estimated originating state ofstimulation and the stimulus parameters, in order to produce a measureof the nerve-to-electrode distance.

According to a further aspect the present invention provides anon-transitory computer readable medium for estimating a distribution offibres recruited by a stimulus, comprising instructions which, whenexecuted by one or more processors, causes performance of the following:

obtaining from at least two sense electrodes spaced apart along a neuralpathway respective measurements of a compound action potentialpropagating along the neural pathway;

determining a conduction velocity of the compound action potential fromthe latency between the measurements, and determining from theconduction velocity a dominant recruited fibre diameter;

determining a rate of dispersion of the compound action potentialbetween the sense electrodes, and determining from the rate ofdispersion a distribution of diameters of the recruited fibrepopulation.

BRIEF DESCRIPTION OF THE DRAWINGS

An example of the invention will now be described with reference to theaccompanying drawings, in which:

FIG. 1 schematically illustrates an implanted spinal cord stimulator;

FIG. 2 is a block diagram of the implanted neurostimulator;

FIG. 3 is a schematic illustrating interaction of the implantedstimulator with a nerve;

FIG. 4 illustrates the typical form of an electrically evoked compoundaction potential (ECAP) of a healthy subject;

FIG. 5 illustrates stimulus of a nerve and dispersion and measurement ofa response;

FIG. 6 is a plot of computed single fibre action potentials, for 10different fibre diameters;

FIG. 7 illustrates a size distribution of a recruited fibre population;

FIG. 8 is a plot of modelled single fibre action potentials, scaled inamplitude according to the distribution of FIG. 7;

FIG. 9 illustrates the synthetic compound action potential produced bysummation of the scaled potentials of FIG. 8, at various distances awayfrom the stimulus location;

FIG. 10 illustrates the calculated dispersion for a single fibre for anumber of differing electrode-to-fibre separations;

FIG. 11 illustrates the width at half height of the synthetic ECAPs asobserved at increasing distance from the stimulus site;

FIG. 12 is a plot of the slope of peak widths relative to four selectedpopulation distributions;

FIG. 13 illustrates single fibre responses as superimposed at thestimulus site;

FIG. 14 is a plot of the action potential peak width for single fibresof varying diameters;

FIG. 15a is an overlaid plot of experimentally obtained measurements ofa sheep ECAP obtained from spaced apart measurement electrodes, and FIG.15b is a plot of the peak to peak amplitude observed on each suchmeasurement electrode in response to increasing stimulation;

FIG. 16a is a plot of the sheep orthodromic responses' N1 peak width athalf height as a function of the channel number, and FIG. 16b is thecorresponding plot for antidromic responses;

FIG. 17 is a plot of ECAPs recorded from electrodes placed in the sheepepidural space;

FIG. 18 is a plot of the width of the N1 peak plotted against therecording channel number, from the data of FIG. 17;

FIGS. 19a and 19b are plots of ECAPs recorded from 24 electrodes placedin the epidural space of another sheep, in the orthodromic andantidromic direction respectively; and FIGS. 19c and 19d are plots ofresponse amplitude and response peak width for the recordings of FIGS.19a and 19b , respectively;

FIG. 20 plots simulated ECAPs produced at varying nerve-to-electrodeseparation at the site of stimulation, together with experimental datatransformed to the site of stimulation;

FIG. 21 illustrates a best-fit fibre size distribution profile;

FIG. 22 illustrates a synthetic ECAP modelled from the distributionprofile of FIG. 21, together with observed sheep ECAP profiles, atvarious distances from the stimulus site;

FIG. 23 illustrates best fit distribution profiles determined for sheepECAPs observed in response to four different stimulus current levels;

FIG. 24 illustrates a strength-duration curve;

FIG. 25 illustrates an alternative representation of the strengthduration curve, for varying electrode-to-nerve separation;

FIG. 26 is a plot of the Rheobase current against electrode to fibreseparation;

FIG. 27 is a plot of a Rheobase-to-height fitting constant against fibrediameter;

FIG. 28 presents simulated plots of the relationship of increasingseparation upon Rheobase;

FIG. 29 schematically depicts Rheobase measurement; and

FIGS. 30a-30d illustrate another embodiment in which electrode-to-nerveseparation is measured by extracting frequency components of neuralmeasurements.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 schematically illustrates an implanted spinal cord stimulator100. Stimulator 100 comprises an electronics module 110 implanted at asuitable location in the patient's lower abdominal area or posteriorsuperior gluteal region, and an electrode assembly 150 implanted withinthe epidural space and connected to the module 110 by a suitable lead.Numerous aspects of operation of implanted neural device 100 arereconfigurable by an external control device 192. Moreover, implantedneural device 100 serves a data gathering role, with gathered data beingcommunicated to external device 192.

FIG. 2 is a block diagram of the implanted neurostimulator 100. Module110 contains a battery 112 and a telemetry module 114. In embodiments ofthe present invention, any suitable type of transcutaneous communication190, such as infrared (IR), electromagnetic, capacitive and inductivetransfer, may be used by telemetry module 114 to transfer power and/ordata between an external device 192 and the electronics module 110.

Module controller 116 has an associated memory 118 storing patientsettings 120, control programs 122 and the like. Controller 116 controlsa pulse generator 124 to generate stimuli in the form of current pulsesin accordance with the patient settings 120 and control programs 122.Electrode selection module 126 switches the generated pulses to theappropriate electrode(s) of electrode array 150, for delivery of thecurrent pulse to the tissue surrounding the selected electrode(s).Measurement circuitry 128 is configured to capture measurements ofneural responses sensed at sense electrode(s) of the electrode array asselected by electrode selection module 126.

FIG. 3 is a schematic illustrating interaction of the implantedstimulator 100 with a nerve 180, in this case the spinal cord howeveralternative embodiments may be positioned adjacent any desired neuraltissue including a peripheral nerve, visceral nerve, parasympatheticnerve or a brain structure. Electrode selection module 126 selects astimulation electrode 2 of electrode array 150 to deliver an electricalcurrent pulse to surrounding tissue including nerve 180, and alsoselects a return electrode 4 of the array 150 for stimulus currentrecovery to maintain a zero net charge transfer.

Delivery of an appropriate stimulus to the nerve 180 evokes a neuralresponse comprising a compound action potential which will propagatealong the nerve 180 as illustrated, for therapeutic purposes which inthe case of a spinal cord stimulator for chronic pain might be to createparaesthesia at a desired location. To this end the stimulus electrodesare used to deliver stimuli at 30 Hz. To fit the device, a clinicianapplies stimuli which produce a sensation that is experienced by theuser as a paraesthesia. When the paraesthesia is in a location and of asize which is congruent with the area of the user's body affected bypain, the clinician nominates that configuration for ongoing use.

The device 100 is further configured to sense the existence andintensity of compound action potentials (CAPs) propagating along nerve180, whether such CAPs are evoked by the stimulus from electrodes 2 and4, or otherwise evoked. To this end, any electrodes of the array 150 maybe selected by the electrode selection module 126 to serve asmeasurement electrode 6 and measurement reference electrode 8. Signalssensed by the measurement electrodes 6 and 8 are passed to measurementcircuitry 128, which for example may operate in accordance with theteachings of International Patent Application Publication No.WO2012155183 by the present applicant, the content of which isincorporated herein by reference.

The present invention recognises that the amplitude and morphology of anECAP measurement depends on a number of factors, including the quantityof recruited fibres contributing to the compound response, theconduction velocity or diameter of each recruited fibre, the separationof the electrode from the fibres in both the radial direction and theaxial direction relative to an axis of the fibre, and the separation ofthe measurement electrode(s) from the stimulus electrode(s).

Here we present methods to determine the separation of fibres fromstimulation electrodes based on measurement of ECAPs. There are a numberof techniques which can be used to eliminate variables in order toisolate the nerve-to-electrode distance d.

A first such technique is to estimate characteristics of the ECAPresponse as it existed when first evoked directly under or adjacent tothe stimulation electrode 2. In this way, the effect of propagation ofthe response can be eliminated, allowing an estimation of the separationfrom the threshold current and conduction velocity of the fibre. Thus,the present embodiment of the invention recognises that the ECAPresponse as it first existed directly adjacent the stimulus electrode 2is one type of an originating state of stimulation which can be usefulin estimating d.

FIG. 4 illustrates the typical form of an electrically evoked compoundaction potential (ECAP) of a healthy subject. The shape of the compoundaction potential shown in FIG. 4 is predictable because it is a resultof the ion currents produced by the ensemble of axons generating actionpotentials in response to stimulation. The action potentials generatedamong a large number of fibres sum to form a compound action potential(CAP). The CAP is the sum of responses from a large number of singlefibre action potentials. The CAP recorded is the result of a largenumber of different fibres depolarising. The propagation velocity of theaction potential on each fibre is determined largely by the diameter ofthat fibre. The CAP generated from the firing of a group of similarfibres is measured as a positive peak potential P1, then a negative peakN1, followed by a second positive peak P2. This is caused by the regionof activation passing the recording electrode as the action potentialspropagate along the individual fibres. An observed CAP signal willtypically have a maximum amplitude in the range of microvolts.

The CAP profile takes a typical form and can be characterised by anysuitable parameter(s) of which some are indicated in FIG. 4. Dependingon the polarity of recording, a normal recorded profile may take aninverse form to that shown in FIG. 4, i.e. having two negative peaks N1and N2, and one positive peak P1.

In this embodiment, electrical stimuli are delivered to the spinal cord502 by one or more stimulus electrodes denoted E1 in FIG. 5. A desireddegree of recruitment, R_(desired), is input by the user or by a settingmade by a clinician when fitting the device or by any other suitablemeans for defining desired recruitment. R_(desired) is processed by acontroller and selector and passed to a stimulus generator whichgenerates a stimulus to be delivered to the neural tissue by electrodeE1. As will be appreciated, while only a single stimulus electrode E1 isshown in FIG. 5, a bipolar, monopolar or tripolar stimulus may beapplied in conjunction with other stimulus electrodes, not shown. At thestimulus site adjacent to E1 within the spinal cord 202, a neuralresponse 510 is evoked by the stimulus.

The neural response evoked by the stimulus at E1 is a compound responsecomprising the individual responses evoked in a number of fibres, andtakes a form shown at 510. The evoked response 510 propagates along therecruited fibres within the spinal cord 502 away from the stimulus siteadjacent to E1, and in so doing the form or morphology of the compoundresponse alters or decays. Without intending to be limited by theory,the decay in the neural response as it travels is at least in part dueto a spreading of the compound response along the spinal cord 502resulting from each recruited fibre having a conduction velocity whichdiffers from the conduction velocity of other recruited fibres. Thealteration or decay in the morphology of the observed neural response asit travels is also in part due to a spreading of the compound responseacross the cross section of the spinal cord 502 due to the variation indepth of the recruited fibres within the cord 502 at different positionsalong the cord. At a time t₂ the compound response passes senseelectrode E2 and is recorded as having an amplitude and durationindicated at 512, which differs from the form of the response at 510 inthat response 512 is of reduced amplitude and greater width or duration.At a later time t₃, after undergoing further spreading and decay, thecompound response passes sense electrode E3 and is recorded as having anamplitude and duration indicated at 514. Observed response 514 is oflesser amplitude but greater duration then observed response 512.Similarly, at a later time t₄, after undergoing further spreading anddecay, the compound response passes electrode E4 and is recorded ashaving a further decreased amplitude and increased duration as indicatedat 516. Observed response 516 is of lesser amplitude but greaterduration then observed response 514.

It is to be appreciated that the form of each observed response, asshown at 510, 512, 514 and 516, is illustrative. The decay and spreadingobserved in any neural response will depend at least upon thecharacteristics of the fibre population actually recruited by thestimulus, the neurophysiology of the subject, and the distance of theelectrodes from the fibres.

In accordance with the present invention, electrodes E2 and E3 are usedto obtain a first measurement 512 and a second measurement 514 of theneural response evoked by the stimulus, via measurement circuitry 522,524 respectively. The evoked CAP measurements in this embodiment aremade by use of the neural response measurement techniques set out inInternational Patent Publication No. WO2012/155183, with two datachannels recording simultaneous data from the two electrodes E2 and E3.

An improved knowledge of the electrophysiological response may lead toexplanations of the large variability which is observed in outcomes fromSCS and may provide valuable insight into electrode and device design,and improved stimulation algorithms.

Without intending to be limited by theory, it is noted that the totalpotential electric field external to and produced from a single nervefibre, including fast Na, persistent Na and slow potassium channels andmyelin properties, can be modelled by:

${\varphi\left( {x,h,t} \right)} = {\frac{\rho}{{4\pi}\;}{\sum\limits_{n = 0}^{\infty}\frac{I_{m}\left( {t - \frac{x_{n} - x_{0}}{\upsilon}} \right)}{\sqrt{h^{2} + \left( {x - x_{n}} \right)^{2}}}}}$where

h is the distance of the measurement electrode from the fibre

x_(n) is the x co-ordinate of each node of Ranvier

I_(m) is the current produced by each node

t is time

v is the conduction velocity of the fibre.

For very small h, the field amplitude is inversely proportional to h, asthe field is dominated by a single node of Ranvier. As the electrode ismoved away the amplitude decreases and the relationship changes to apower law as the measurement electrode is influenced by the fieldsproduced by more nodes. The shape of the action potential also changeswith distance to the measuring electrode. The action current I_(m) isweighted and summed at the measurement electrode, but with differentdelays for each of the nodes x_(n). The weights change because of theincrease in distance from the node to the electrode. This looks like afilter (I/r).

Several suitable models exist for assessing single fibre behaviour, suchas models based on Hodgkin Huxley cable models, and any such singlefibre model may be used in embodiments of the present invention. Withsuitably chosen parameters for the ion channel gating functions, FIG. 6is a plot of computed single fibre action potentials, for 10 differentfibre diameters from 19 μm to 8.7 μm. Specifically, plot 602 shows thecomputed single fibre action potential for a 19 μm diameter fibre, andplot 604 shows the computed single fibre action potential for a 8.7 μmdiameter fibre. The large diameter fibres conduct at the highestvelocity and the smaller diameter fibres have progressively longerlatency and are progressively smaller in size. To calculate a compoundaction potential requires an estimate of the number of fibres for eachsize of fibre. The compound action potential is then simply the sum ofcontributions from all those fibres. That is, the ECAP consists of thecontributions of the electrical activity from all the recruited fibers,where the response from a single fiber is referred to as the singlefiber action potential (SFAP).

Calculations were made with the modelled measurement electrodepositioned from 35 mm to 84 mm away from the stimulation electrode alongthe neural pathway, at increments of 7 mm. Both the measurement andsense electrodes are modelled as being located directly above, andseparated by a nominated distance (h) from, the modelled fibre. Apopulation distribution was generated as a function of fibre diameter,as shown in FIG. 7, in which the Y axis is an arbitrary scale plottedagainst the diameter of the fibre. The population distribution of FIG. 7comprises fibres as small as 15 μm, up to 21 μm, in the relativeproportions shown.

FIG. 8 is a plot of each of the single fibre potentials, scaled by thepopulation distribution of FIG. 7 for the modelled fibre diameters, at asingle location. The electrode-to-nerve distance was modelled as 6 mm,and FIG. 9 illustrates the synthetic compound action potentialcalculated at multiple electrode locations by summation of the singlefibre responses at each electrode location such as those shown in FIG. 8for a single location. In particular, FIG. 9 shows such a syntheticcompound action potential as observed at each of the electrodespositioned along the nerve and 6 mm away from the nerve, and at adistance of 35 mm to 84 mm away from the stimulus site, respectively.Specifically, plot 902 shows the computed compound action potential asobserved at the electrode 35 mm away from the stimulus site, and plot904 shows the computed compound action potential as observed at theelectrode 84 mm away from the stimulus site, with interposed plots shownfor respective interposed electrodes. As can be seen in FIG. 9, thesimulated compound action potential decays (reduces in amplitude) anddisperses (widens) as it travels away from the stimulus site.

A convenient measure of the dispersion of the ECAP is to measure widthof the N1 peak at half height, as indicated at 410 in FIG. 4. Theobserved dispersion is related to the separation of the measurementelectrode from the fibre, whereby for a given single action potential orcompound action potential a narrower dispersion is observed at a smallerelectrode-to-fibre separation and a wider dispersion is observed at alarger separation. This is a result of the previously discussed effectthat the closer the electrode is to the fibre, the more the signalobserved by the sense electrode is dominated by the nodes of Ranvierthat are closest to the electrode. As the electrode-to-fibre distanceincreases, the signal present at the sense electrode becomes influencedby more nodes of Ranvier positioned along the fibre, dispersing theobserved response. This effect sums over many fibres and thus alsooccurs when measuring contributions from many fibres as is the case inECAP measurement. However the observed dispersion also depends on thecontribution from fibres of different diameter, which each conduct atdifferent velocities. The present embodiment recognises that therelative influence of the fibre population distribution, on one hand,and the relative influence of the height above the cord, on the otherhand, can be separated.

FIG. 10 illustrates the calculated dispersion for a single fibre, beingthe width 410 of the N1 peak at half height, for a number of differingelectrode-to-fibre separations. The relationship is linear and varies bya factor of 4 over the range of separations calculated. However inpractice recruitment of a single fibre by device 100 is impossible andthe contribution of multiple recruited fibres, of varying diameter, mustbe taken into account for any practical observations. To this end,synthetic ECAPS were generated for a number of differing fibrepopulations, for two cases: measurement electrodes positioned at 3 mmabove the axon, and at 6 mm above the axon. FIG. 11 illustrates thewidth at half height of the resulting synthetic ECAPs as observed atchannels (electrodes) 5 through 16 at increasing distance from thestimulus site.

As can be seen in FIG. 11, the plot of dispersion of the ECAP variesconsiderably with changes in the recruited fibre population, even forunchanged electrode-to-nerve separation. For synthetic observations1110, which all relate to an electrode-to-nerve separation of 6 mm, thevariation in recruited fibre population can give dispersion as little as50 μs between channel 5 and 16 in the case of observation 1112, or aslarge as 100 μs between channel 5 and 16 in the case of observation1114. The modelled fibre population distributions at each heightcomprise a distribution width of 6, 7, 8 or 9 μm, whereby a distributionwith an increased number of smaller fibres, and having fibres of asmaller diameter, gives rise to an increased slope of the width at halfheight of the N1 peak in relation to the propagation distance. Similarvariation can be seen in the synthetic observations 1120, which allrelate to an electrode-to-nerve separation of 3 mm, for the same fourselected fibre distributions.

FIG. 11 shows that the width at half depth of the N1 peak, and thus theCAP dispersion, has a linear dependence on the propagation distance,increasing with propagation distance due to impact of the smallerdiameter fibres travelling at slower speeds and increasing the width ordispersion of the peak.

FIG. 12 is a plot of the slope, in ms per channel, of the peak widthsrelative to the four selected population distributions from the samedata as FIG. 11. As can be seen, as the population distributions arewidened by the addition of smaller fibres, the resulting dispersionincreases.

Thus dispersion alone cannot be used to determine electrode to nerveseparation because the recruited fibre population's size distribution isan unknown. However, referring again to FIG. 11, the present embodimentrecognises that a line or curve fitted to the observed ECAP peak widthsand extrapolated to the stimulus site (channel “0” in FIG. 11), gives avalue which is substantially independent of the propagation dispersioneffects. In particular, all of the curves 1110 meet the y-axis of FIG.11 at substantially a first point around 125 μs, while all of the curves1120 meet the y-axis at substantially a second point around 60 μs.Accordingly, in this embodiment the intercept of the lines 1102 or 1104with the y-axis at channel “0” is taken as the originating state ofstimulation. Importantly, propagation dispersion is effectivelyeliminated by determining the y-intercept. The present embodimentrecognises that the y-intercept value of the lines varies withelectrode-to-nerve separation. Moreover, the y-intercept can be obtainedin practice as simply as by applying one stimulus and obtaining aslittle as two measurements of the ECAP at spaced-apart sense electrodes,as a line can be fitted to two such data points to estimate ay-intercept. Other embodiments may obtain many sense electrodemeasurements of a single ECAP in order to improve accuracy, or maydetermine the y-intercept by any suitable means.

It is further to be noted that the y-intercept value of the lines 1110and 1120 is impossible to measure directly in practice, as the stimulusapplied at the stimulus site is many orders of magnitude larger than theresponse evoked.

Accordingly, in some embodiments changes in the y-intercept may be usedto indicate relative changes in the electrode-to-nerve distance d, evenif the absolute value of d is not known.

However, other embodiments further provide for an estimation of theabsolute value of the distance d, as follows. These embodiments arebased on the recognition that the ECAP peak width at Channel 0 (beingthe stimulus location) is dominated by the width of the single fibreaction potential of the largest recruited fibre contributing to theresponse. For a given nerve, the largest recruited fibre is typicallythe most easily recruited and can thus be assumed to have been recruitedif any ECAP at all is evoked. The action potential peak width of thelargest recruited fibre is a constant, but will be observed as a broaderpeak with increasing fibre to electrode distance d. Thus, the peak widthof the observed response at channel 0 is dependent on the separation dbut is substantially independent of the population distribution of thefibres recruited, at least for the range of populations simulated inFIG. 11.

FIG. 13 shows the action potentials calculated for individual fibresover a range of fibre diameters from 18 micron (SFAP 1302) to 23 micron(SFAP 1304), with intervening fibres' action potentials shown but notlabelled. The sum of the SFAPs produces the larger CAP 1306. As shown inFIG. 13, the larger diameter fibres produce the largest SFAP responses.When mapped to the stimulus site, the smaller diameter fibres at Channel0 contribute responses to the compound response 1306 which are envelopedby, or do not significantly affect some key characteristics of, thesingle fibre response 1304 of the largest contributing fibre diameter.

FIG. 14 is a plot of the single fibre action potential peak width, forsingle fibres of varying diameters in the range 11-23 μm, as indicatedby square data points. The circular data point 1402 indicates thesynthetic compound action potential peak width occurring at channel 0for the population of fibres shown in FIG. 7. As can be seen from 1402,the 20 μm fibre was the most abundant in this population distributionand the peak width of the ECAP at 1402 was 1.3×10⁻⁴ s whereas the widthof a single 20 μm fibre response was 1.27×10⁻⁴ s, which is a 2% error inthe approximation. The error gets worse with wider distributions offibre diameters in the fibre population. With a range of fibres from 14μm to 23 μm in diameter the width at half depth is 4% larger than thevalue for the SFAP. The net effect is that the present technique willslightly overestimate the separation of electrode from the respondingfibre when the relation evident in FIG. 14 is used to calculate thecorresponding distance.

To verify the above theoretical approach, animal (sheep) experimentswere conducted by epidural implantation of a 24 channel linear electrodearray with electrode spacing of 7 mm. Current sources were configured toproduce tripolar stimulation with a central cathode (channel 2) andanodes on each side (channels 1 & 3). Evoked responses were recorded onelectrodes 4 to 24. FIG. 15a is an overlay of all of the recordings fromchannels 4 to 24 in response to stimulation at 0.7 mA. FIG. 15b is aplot of the peak to peak amplitude observed on each electrode 4 to 24 inresponse to increasing stimulation from 0.4 mA to 1.0 mA.

The ECAP peak width, defined here as the width at half height of theobserved N1 peak, was determined on all channels, at various stimulationcurrent levels. FIG. 16a is a plot of the sheep orthodromic responses'N1 peak width at half height as a function of the channel number forstimulation currents of 1 mA (squares), 0.9 mA (circles) and 0.8 mA(triangles). FIG. 16b is the corresponding plot for the antidromicresponses' N1 peak width at half height as a function of the channelnumber, for stimulation currents of 1.106 mA (squares), 0.996 mA(circles) and 0.801 mA (triangles). Raw neural response measurement datawas interpolated in order to remove sampling quantisation effects andimprove the estimates of peak width. In each plot the straight line isfrom least squares fit of the data for all the measurements averaged foreach channel. FIG. 16 shows that the relationship of the width at halfheight of the responses with the channel number is substantiallyindependent of the stimulation current. Thus the approach ofextrapolating such data to the stimulus channel location (channel 2) isrobust to variations in stimulation current and/or to movement inducedchanges in the recruitment efficacy of a given current.

In FIG. 16 the width at half height (HH) of the responses in theorthodromic direction have a slope with channel number of 5.2×10⁻⁶, andin the antidromic direction the slope is 5.5×10⁻⁶, which demonstratesthat the fibres which are responding in both antidromic and orthodromicdirections have similar distributions of fibre diameters.

In FIG. 16a the stimulus channel is channel 2 so that the originatingstate of stimulation of interest in this embodiment is the peak width atchannel 2. Extrapolating the channel 5-20 orthodromic data back to thesite of channel 2 gives an estimated channel 2 peak width of 0.00014 s(140 μs). In FIG. 16b the stimulus channel is channel 20 so that theoriginating state of stimulation of interest in this embodiment is thepeak width at channel 20. Extrapolating the channel 2-17 antidromic databack to the site of channel 20 gives an estimated channel 20 peak widthof 0.000125 s (125 μs). Taking the average of the orthodromic estimateand the antidromic estimate, and comparing to FIG. 10, allows theaverage electrode-to-fibre distance along the array to be estimated atabout 5 mm.

In another experiment ECAPs were recorded from electrodes placed in thesheep epidural space for a stimulation current of 1 mA 40 μs pulse widthbiphasic stimuli. The wave form measured on a single electrode has aduration of less than 1.5 ms and the recordings on electrodes which area short distance from the stimulation electrode are truncated by theblanking period of the amplifier and presence of the stimulus current.FIG. 17 shows the obtained recordings. FIG. 18 is a plot of the width ofthe N1 peak plotted against the recording channel number, from the dataof FIG. 17. As shown by fitted line 1802, the width of the N1 peak islinear with the propagation distance across the first 4 electrodes(channels 3-6). As shown by fitted line 1804 the width of the N1 peak isalso linear for the next four electrodes (channels 7-10) albeit with adifferent, smaller, slope. A corresponding fitted line could be fittedto the final few electrodes, channels 12-14. The y-intercept of lines1802 and 1804 is, notably, the same: 0.12 ms (120 μs). This representsthe width of the ECAP if it could be recorded under the stimulatingelectrode. Some embodiments of the invention may thus fit a plurality oflines to the ECAP width or dispersion measurements, being one linefitted to each subset of electrodes positioned within each respectivevertebral segment. Such embodiments reflect the fact thatdiscontinuities in dispersion appear with propagation distance,accompanied by a change in the slope of the dispersion towards smallerslopes, due to the removal of smaller diameter slower conducting fibresfrom the recruited population as such fibres terminate at each crossingbetween vertebral segments. In such embodiments the plurality of fittedlines may each be extrapolated to the stimulus location to estimate theoriginating peak width, and/or the fitting of such lines may beconstrained by a requirement that each line must intersect all others atthe stimulus channel, to thereby improve the robustness of themulti-line fitting estimate of the originating state of stimulation, ascompared to a single line fitting. In FIG. 18 it can be seen by visualinspection that channel 11 most likely is adjacent a vertebral segmentcrossing in a region where only a subset of that segment's terminatingfibres have in fact terminated, so that channel 11 is not clearlygrouped with either channels 7-10 nor channels 12-14. Some embodimentsmay seek to identify and discard such vertebral segment crossing datapoints when fitting lines 1802, 1804, etc.

To further study this effect a 24 channel electrode was implanted inanother sheep and antidromic and orthodromic responses were measured,with results shown in FIG. 19. Stimulation was tripolar, biphasic. ForFIG. 19c stimulation was delivered from a cathode on electrode 2 andanodes on channel 1 and 3, and recording electrodes from 5 to 20. ForFIG. 19d stimulation was delivered from a cathode on electrode 20 andanodes on channel 19 and 21, and recording electrodes from 2 to 17.FIGS. 19c and 19d show that the discontinuities in the dispersion whichappear with the propagation distance arise in both the orthodromic andantidromic conduction directions, consistent with the neuroanatomy ofthe spinal cord. The present technique may thus be used to assesselectrode height not only when stimuli are delivered at the caudal endof the array, but also when stimuli are delivered at the rostral end ofthe array. When stimuli are delivered from part way along the array,recording electrodes positioned both caudally and rostrally of thestimulus electrode(s) may be used to provide both orthodromic andantidromic estimates of ECAP dispersion to give a combined estimate ofthe originating ECAP peak width and the electrode height. In the studyof FIG. 19 there were 4-5 electrodes spanning a single vertebral segmentand recordings were made across 4 vertebral segments. It is evident whencomparing the upper and lower portions of FIG. 19c , and of FIG. 19d ,that both the dip or cornerpoint in the amplitudes and the change inslope of the dispersion plot correspond with the fibres crossing fromone verterbral segment to the other. The data points indicated bytriangles, squares and circles in the lower plots of FIGS. 19c and 19dreflect dispersion data obtained in response to stimuli of differingamplitude. Fitted lines 1902, 1904, 1906 and 1908 correspond to eachvertebral segment and, despite having different slope, each have thesame value at the stimulus electrode, channel 2. The multiple linesfitted to the antidromic data of FIG. 19d also have a shared interceptat the stimulus electrode on channel 20, around 0.11 ms, allowingresponse peak width at the site of the channel 20 stimulus to berobustly estimated, and in turn allowing relative or absoluteelectrode-to-nerve separation to be measured as discussed elsewhereherein.

Thus, the above approach allows an absolute value of theelectrode-to-fibre distance to be estimated solely from electrical ECAPmeasurements.

To further test the validity of the 5 mm separation estimate obtainedabove in relation to FIG. 16, the theoretical “channel 0” responsesevoked by an electrode positioned at 2 mm, 5 mm, 8 mm and from a nervefibre were simulated. In FIG. 20, the continuous curve 2002 is thesimulated response at 2 mm separation, continuous curve 2004 is thesimulated response at 5 mm separation, and 2006 is the simulatedresponse at 8 mm separation. The experimental data points shown in FIG.20 are produced by taking the experimental data of FIG. 15a , timescaling each channel's observed response to have a peak width equal tothe experimentally determined “channel 0” peak width, removing thepre-response latency at that electrode as defined by conduction velocityand electrode distance from the stimulus site by temporally aligning theN1 peak of each response, and normalising the N1 amplitude. As can beseen in FIG. 20, the experimentally observed responses when scaled inthis manner (a) take substantially the same profile as each other, and(b) coincide very closely with the simulated channel 0 response 2004which is evoked by the simulated electrode when at a 5 mm spacing fromthe fibre, thereby verifying the estimate of 5 mm produced above.

Another embodiment of the invention further recognises that FIGS. 6-14reveal a means by which the size distribution of fibres recruited by asingle stimulus may be estimated from ECAP measurements. Referring toFIGS. 11 and 12, it can be seen that for a given fibre populationdistribution, the observed slope of the ECAP peak width depends onelectrode-to-fibre distance, the slope being larger when the distance dis smaller.

A further variable which affects the dispersion, or growth in peakwidth, is the conduction velocity of the recruited fibre. However theconduction velocity can be determined from the latency of the measuredresponses as is visible in FIG. 15a in which the velocity of the N1 peakis 116 ms⁻¹. The SFAP which conducts at this velocity in the model has adiameter of 21 μm, which is consistent with the diameter versusconduction velocity slope of 5.4 which has been reported.

Thus, the conduction velocity observed in FIG. 15a enables adetermination to be made as to the diameter of the most abundant fibrein the recruited fibre population, in this case 21 μm. Next, the slopeof the width at half height observed in FIGS. 16a and 16b enables therelationship shown in FIG. 12 to be used to estimate the distribution ofrecruited fibres. Finally, a profile of the distribution of recruitedfibres may be produced. This involves taking a nominal distributionprofile, and summing the individual fibre contributions to a simulatedECAP using a chosen single fibre model, and fitting the simulated ECAPto an observed ECAP by trial and error adjustment of the nominalprofile, until a best fit is found. In the case of the sheep data ofFIG. 15a , the best fit fibre distribution profile determined in thismanner is shown in FIG. 21. FIG. 22 comprises plots 2202 of thesimulated ECAP resulting from single fibre modelling and summation of arecruited fibre distribution having the profile shown in FIG. 21,together with plots 2204 of the actual observed sheep ECAP data, asobserved at electrodes at distances from 35 mm to 84 mm away from thestimulus site. As can be seen, the best fit fibre distribution profileof FIG. 21 when simulated results in a close fit of the simulated ECAP2204 to the observed sheep ECAP 2202, and such fitting thus enables thefibre distribution profile to be estimated. Any suitable fittingtechnique, such as a pointwise least squares fitting, may be applied todetermine which nominal fibre distribution profile gives the best fit toan observed ECAP.

Accordingly, some embodiments of the invention may additionally oralternatively seek to use response dispersion to estimate the recruitedfibre population's dominant fibre size, and also the width of thedistribution of fibre sizes recruited.

Thus the response of the sheep spinal cord to SCS demonstrates aconsistent increasing distribution of fiber velocities with increasingcurrent. These techniques are also applicable to use in humans, wheredetailed understanding of the electrophysiological response of thespinal cord to electrical stimulation, and the distribution of fiberdiameters in chronic pain sufferers, may lead to better diagnostic andpatient programming outcomes.

The effect of increasing the stimulation current, as observed in FIG.15b , on the profile of the best-fit distribution was also determined.The best fit distribution profiles determined for each current level areshown in FIG. 23. FIG. 23 shows that the population of responding fibresvaries with the changes in current, and in particular as the current isincreased the proportion of smaller diameter (18-19 μm) fibrescontributing to the ECAP is expected to increase.

Moreover, once the fibre distribution characteristics are known,including the dominant fibre size recruited (in FIG. 23 being 20-21 μm),distribution width (17-23 μm) and distribution profile (as shown in FIG.23), single fibre modelling and summation even enables the number offibres of each size which are being recruited to be estimated, byamplitude comparison to the observed ECAP. Thus, as shown in the y-axisof FIG. 23 it can be determined for the sheep data that at peak currentabout 300 18 μm fibres were recruited and about 550 21 μm fibres wererecruited, for example. Similarly, the total number of fibres recruitedis simply the integral of the population distribution curve and for thesheep spinal cord the total number of recruited fibres is 2080 fibres at1.0 mA, 1780 fibres at 0.9 mA, 1440 fibres at 0.8 mA and 545 fibres at0.7 mA.

In yet another embodiment, a technique which can be used to estimate thenerve-to-electrode distance d involves probing the Rheobase bydelivering appropriate stimuli and measuring the neural responsesthereto.

A plot of the threshold current required to evoke a response against thepulse width is a strength duration curve as shown in FIG. 24. TheRheobase current is defined as the maximum current at infinite pulsewidth which doesn't evoke a response. The present embodiment recognisesthat the Rheobase current depends on the separation of the electrodefrom the nerve, so that the curve of FIG. 24 shifts towards the originfor a small separation, and shifts away from the origin (up and to theright in FIG. 24) for larger separations.

FIG. 25 comprises an alternative representation of the strength durationcurve of FIG. 24, by plotting applied charge against pulse width, for a10 micron diameter fibre. Further, this figure includes a plot at anumber of electrode separations from the fibre, namely a plot 2502 for aseparation of 3 mm, 2504 for 4 mm, 2506 for 5 mm, 2508 for 6 mm, 2510for 7 mm and 2512 for 8 mm. In this representation of the strengthduration curve, each curve is substantially linear and the slope isequal to the Rheobase current.

FIG. 25 allows a plot, shown in FIG. 26, to be derived which representsthe relationship of the Rheobase current R to the separation h from thefibre. In this instance of a simulated single fibre diameter, the fittedrelationship is R=Bh{circumflex over ( )}A, where A and B areempirically fitted constants. Here A=0.5385 and B=10e3.485.

This process by which FIG. 26 was obtained for a single fibre model of afibre diameter of 10 microns was then repeated for multiple fibrediameters D, namely D=[7, 8, 9, 10, 11, 12] microns. For these singlefibre sizes, the fitting constants A were respectively calculated astaking the values A=[0.55, 0.537, 0.532, 0.5385, 0.53, 0.51]. Thisindicates that A is approximately constant with changing fibre diameterat least throughout this range, the average value of A being 0.5329.

On the other hand, the fitting constants B were respectively calculatedas taking values B=[3.399, 3.445, 3.472, 3.485, 3.493, 3.507]. Thisindicates that B is monotonic increasing with increasing fibre diameter,at least in this fibre diameter range. FIG. 27 plots the values of Bagainst fibre diameter, and also shows a straight-line-fit to the datapoints, having the equation B=0.01991 D+3.278, where D is the diameterof the fibre.

Thus, this embodiment applies stimuli of varying pulse width from afirst stimulus electrode to determine at least two points on thestrength-duration curve, as it exists for the unknown separation h. Fromtwo such points, the Rheobase R for the first-recruited fibre can becalculated in respect of the first stimulus electrode. Because fibrediameter D is unknown, the Rheobase R alone does not yield h.

FIG. 28 shows simulated plots of the relationship of increasingseparation upon the expected Rheobase value. As expected, Rheobasegenerally increases as electrode-to-nerve distance increases. However,for each single fibre diameter, the relationship follows a curve and notlinear, and moreover at any given separation the Rheobase value of onefibre diameter differs from a differing fibre diameter. As the observedresponse is a compound action potential, at any given separation thefirst-recruited fibre will always be the same, being the largest mostproximal fibre to the stimulus electrode. That is, the separation vsRheobase relationship for the observable compound response will be thesame as the curve 2802 of the largest most easily recruited fibre.

The present embodiment thus further provides for determining aconduction velocity of the evoked response at threshold, as conductionvelocity is well related to fibre diameter. For example two senseelectrodes spaced apart along a neural pathway may record a time ofarrival of an evoked response in order to determine the conductionvelocity V. The recruited fibre diameter D can then be determined by theempirically determined relationship D=V/X, where X is typically ascribeda value around 5.4-6. Knowing D, B can be deduced from FIG. 27. Nowknowing R, B and A, the equation R=Bh{circumflex over ( )}A can besolved to give the electrode to fibre separation h, as desired. In thisembodiment the originating state of stimulation is thus the Rheobase,for which an observable characteristic is defined by a single fibre sizeas demonstrated by reference to FIG. 28.

In other embodiments, rather than a straight line fit, a curve may befitted to the data points of FIG. 27 to improve B estimation, and suchembodiments are within the scope of the present invention.

There are a number of ways to measure the Rheobase dynamically and inreal time such as during SCS. As described previously the Rheobasecurrent can be estimated from the slope of the charge duration curve.The slope estimation requires at least two points along this curve, andto obtain these two points requires estimation of the threshold ofresponse for two different stimulus durations. The threshold measurementcan be made in a number of ways, and a simple way to make thismeasurement, schematically depicted in FIG. 29, is to measure the slopeof the amplitude of the ECAP with respect to stimulation current, toestimate a threshold current. Determination of the threshold at twopulse widths provides the data necessary to compute the Rheobasecurrent. Thus in this method four stimuli are required, but at least twoof the stimuli can be controlled to have the same charge as a requiredtherapeutic level, and thus provide therapeutic stimuli. The other twostimuli required to complete the Rheobase measurement can then be lowerin amplitude and thus not uncomfortable and may even be below aperception threshold.

It is to be appreciated that the stimuli sequence could be appliedcontinuously and the Rheobase calculated continuously and averaged overtime, or further signal processing techniques applied to improve the SNRof this measure. The conduction velocity needs only be measuredinfrequently and for many applications can be measured only once, or onrare occasions, to provide the remaining constant.

FIGS. 30a-30d illustrate another embodiment of the invention, in whichECAP dispersion, and electrode-to-nerve separation, are measured orassessed by extracting frequency components of the neural measurements,by fast Fourier transform. The neural measurements are first windowed toexclude discontinuities or like stimulus effects and/or measurementeffects. The frequency domain information of the respective neuralmeasurements may then be used to extract a measure of the dispersion.FIG. 30a plots simulations of the ECAP of a 12 μm diameter fibremeasured 35 mm away from the stimulating site and at separations of 2,3, 4, 5 and 6 mm, respectively, between the electrode and the fibre.Once again, both the amplitude and the dispersion of the observedresponse changes with separation, with larger separations producingsmaller more dispersed responses. FIG. 30b shows the Fourier spectrum ofthe data from the first figure (Haming window). The present embodimentoperates by noting that the decay in the frequency response of eachobserved ECAP at frequencies higher than the peak is linear. It is alsonoted that the peak amplitude of each curve in FIG. 30b , and thespectral spread of each curve, reflects the sharpness of the observedresponse, and either or both such measures may thus be used as a measureof the inverse of response dispersion. FIG. 30c shows the slope of thedecay of frequency contributions to each respective observed response,at frequencies higher than the peak of the respective curve. The presentembodiment further notes that the slope of the decay of each curve isproportional to the separation of the fibre from the electrode, wherebya steeper decay slope corresponds to greater dispersion and thus greaterseparation. FIG. 30d is a plot of decay slope against separation,indicating the monotonic nature of this relationship in the separationsobserved, and for example FIG. 30d may be reflected in a lookup tablewhereby the spectral decay slope observed in a given response may beused to look up electrode-to-nerve separation. Such embodiments may beadvantageous in measuring dispersion in noisy neural measurements, as afrequency roll-off can be averaged or fitted over a relatively widespectral range. Such embodiments may further be advantageous in enablinga measure of dispersion to be obtained without reliance on the amplitudeof the ECAP, for example in embodiments where manual user feedback orautomated feedback operates to control recruitment at a substantiallyconstant level.

The stimulation electrodes and sensing electrodes in one embodiment arean array of electrodes. The stimulus location and the measurementlocation could be changed from one measurement to the next, such as bybeing scanned across the array with electronic switching means, and theRheobase/distance computed in real time and from this a two dimensionalpicture of the underlying neural active elements and their location withrespect to the electrodes of the array could be determined.

An image so produced could in turn be used to guide a surgicalprocedure, such as the removal of tissue with little or no response suchas is performed in DREZ lesion surgery, or detection and removal ofaberrantly responding tissue such as the removal of brain lesionsresponsible for focal origin epilepsy.

The geometry of the sensing stimulating electrodes need not be planarbut may be circumferential to a neural structure such as those employedin cuff electrodes. Electrodes spaced around the circumference of amajor nerve, for instance the vagal nerve could use the techniquesdescribed above to provide estimates as to the locations of individualfascicles within the nerve bundle. It is highly desirable to be able toaddress individual fascicles with stimulation and a knowledge of thefascicle geometry and arrangement could, via current steering or othermeans, provide selective stimulation.

The fascicles in major nerves do not run a linear course through thenerve. For example, examination of serial cross sections of the nerve atdifferent positions along the nerve would reveal that individualfascicles at the centre of the bundle in one section could be found atthe edges in another section. This observation, combined with the hereindescribed techniques to map the separation of electrode to activetissue, could be used to choose effective electrodes or be used toappropriately place a cuff electrode on a nerve during surgery.

It will be appreciated by persons skilled in the art that numerousvariations and/or modifications may be made to the invention as shown inthe specific embodiments without departing from the spirit or scope ofthe invention as broadly described. The present embodiments are,therefore, to be considered in all respects as illustrative and notlimiting or restrictive.

The invention claimed is:
 1. An implantable device for estimating anerve-to-electrode distance, the device comprising: at least onestimulus electrode and at least one sense electrode; measurementcircuitry for obtaining a neural measurement from the at least one senseelectrode; and a processor configured to: apply from the at least onestimulus electrode to a nerve at least one stimulus having definedstimulus parameters; obtain from the measurement circuitry a pluralityof neural measurements of at least one compound action potential evokedby the at least one stimulus; process the plurality of neuralmeasurements in order to estimate an originating state of stimulation,the originating state of stimulation exhibiting at least one observablecharacteristic defined by a single fibre size; and apply a single fibremodel to the estimated originating state of stimulation and the stimulusparameters, in order to produce a measure of the nerve-to-electrodedistance.
 2. The implantable device for estimating a nerve-to-electrodedistance of claim 1, wherein the measure of the nerve-to electrodedistance comprises an absolute measure of distance.
 3. The implantabledevice for estimating a nerve-to-electrode distance of claim 1, whereinthe measure of the nerve-to electrode distance comprises a relativemeasure reflecting a change in distance from a previous time.
 4. Theimplantable device for estimating a nerve-to-electrode distance of claim1, wherein the processor is further configured to adjust a therapeuticstimulus regime in response to an observed change in thenerve-to-electrode distance.
 5. The implantable device for estimating anerve-to-electrode distance of claim 1, wherein the single fibre modelcomprises a lookup table matching the observed characteristic and thestimulus parameters to a corresponding nerve-to-electrode distance. 6.The implantable device for estimating a nerve-to-electrode distance ofclaim 1, wherein the implantable device functions intra-operatively, aspart of a surgical procedure.
 7. The implantable device for estimating anerve-to-electrode distance of claim 6, wherein the processor isconfigured to performed to progressively monitor a position of astructure bearing the electrodes relative to the nerve.
 8. Theimplantable device for estimating a nerve-to-electrode distance of claim6, wherein the processor is configured to image fibres of the nerve. 9.The implantable device for estimating nerve-to-electrode distance ofclaim 1, wherein the implantable device functions as part of apostoperative fitting procedure of a neurostimulator.
 10. Theimplantable device for estimating nerve-to-electrode distance of claim1, wherein the originating state of stimulation comprises an estimatedECAP peak width at the stimulus site.
 11. The implantable device forestimating nerve-to-electrode distance of claim 10, wherein to apply asingle fibre model to the estimated originating state of stimulation andthe stimulus parameters, in order to produce a measure of thenerve-to-electrode distance, the processor is configured to apply asingle stimulus in order to evoke a single ECAP, and wherein theplurality of neural measurements are obtained from at least two senseelectrodes each at a unique distance away from the stimulus electrode.12. The implantable device for estimating nerve-to-electrode distance ofclaim 10, wherein the processor is further configured to estimate anoriginating ECAP peak width by extrapolating a first ECAP measureobtained from a first sense electrode and a second ECAP measure obtainedfrom a second sense electrode back to the stimulus site.
 13. Theimplantable device for estimating nerve-to-electrode distance of claim12, wherein the originating ECAP peak width is taken as being dominatedby a single fibre of largest diameter, and the processor is furtherconfigured to determine the nerve-to-electrode distance from therelationship of the single fibre originating peak width tonerve-to-electrode distance.
 14. The implantable device for estimatingnerve-to-electrode distance of claim 10, wherein the measure of ECAPpeak width comprises a half-height peak width, being a measure of awidth of an ECAP peak as observed at an amplitude which is half theamplitude of the peak amplitude of the observed ECAP peak.
 15. Theimplantable device for estimating nerve-to-electrode distance of claim10, wherein the measure of ECAP peak width comprises a time betweenpeaks of the observed response.
 16. The implantable device forestimating nerve-to-electrode distance of claim 10, wherein the measureof ECAP peak width comprises a time between a first zero crossing and asecond zero crossing of the neural measurement.
 17. The implantabledevice for estimating nerve-to-electrode distance of claim 1, whereinthe processor is further configured to obtain neural measurements ofboth orthodromic and antidromic ECAPs, to improve an estimate of theoriginating state of stimulation.
 18. The implantable device forestimating nerve-to-electrode distance of claim 1, wherein theoriginating state of stimulation comprises a Rheobase.
 19. Theimplantable device for estimating nerve-to-electrode distance of claim18, wherein the processor is further configured to determine a stimulusthreshold at at least two differing stimulus pulse widths, and whereinthe Rheobase is calculated from the stimulus thresholds.
 20. Theimplantable device for estimating nerve-to-electrode distance of claim18, wherein a conduction velocity is measured and used to determine afibre diameter recruited at threshold.
 21. The implantable device forestimating nerve-to-electrode distance of claim 20, wherein a fittedrelationship of the modelled single fibre diameter Rheobase to theelectrode-to-nerve separation is used to determine the separation.